{"id":66913,"date":"2026-10-13T10:13:07","date_gmt":"2026-10-13T07:13:07","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66913"},"modified":"2026-10-13T10:13:07","modified_gmt":"2026-10-13T07:13:07","slug":"kirchhoffs-law-of-thermochemistry-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/kirchhoffs-law-of-thermochemistry-calculator\/","title":{"rendered":"Kirchhoff's Law of Thermochemistry Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Adjust a Reaction Enthalpy from One Temperature to Another<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66913\" data-favorite-title=\"Kirchhoff&#039;s Law of Thermochemistry\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/kirchhoffs-law-of-thermochemistry-calculator\/\" data-favorite-excerpt=\"Convert a reaction enthalpy from one temperature to another using Kirchhoff&#039;s law. Enter the known enthalpy at a reference temperature, the target temperature, and the summed heat capacities of reactants and products.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-chemistry-1\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/chemistry\/kirchhoffs-law-of-thermochemistry-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66913\" data-post=\"66913\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">Enthalpy at the Reference Temperature<\/span><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Reaction Enthalpy at Reference Temperature (\u0394H\u2081)<\/label><div class=\"term\">\u0394H\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"number\" name=\"reaction_enthalpy_at_reference_temperature_h\" id=\"field-2\" aria-describedby=\"calc-info-2\" placeholder=\"e.g. -92.2\" step=\"any\" value=\"-92.2\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unit\" aria-label=\"Unit\"><option value=\"kJ_mol\" selected>kJ\/mol<\/option><option value=\"kcal_mol\">kcal\/mol<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-2\">Standard reaction enthalpy (e.g. \u0394H\u00b0f at 298.15 K). Negative for exothermic, positive for endothermic reactions.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-4\">Reference Temperature (T\u2081)<\/label><div class=\"term\">T\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"reference_temperature_t\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 298.15\" min=\"0\" value=\"298.15\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"unit\" aria-label=\"Unit\"><option value=\"K\" selected>K<\/option><option value=\"C\">\u00b0C<\/option><option value=\"F\">\u00b0F<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-4\">Temperature at which \u0394H\u2081 is known \u2014 usually the standard reference temperature 298.15 K (25 \u00b0C).<\/small><\/div><div class=\"is-single field\" id=\"input-4\"><span class=\"font-semibold\">Target Temperature<\/span><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-7\">Target Temperature (T\u2082)<\/label><div class=\"term\">T\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"target_temperature_t\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 400\" min=\"0\" value=\"400\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"unit\" aria-label=\"Unit\"><option value=\"K\" selected>K<\/option><option value=\"C\">\u00b0C<\/option><option value=\"F\">\u00b0F<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-7\">Temperature at which the reaction enthalpy should be estimated.<\/small><\/div><div class=\"is-single field\" id=\"input-6\"><span class=\"font-semibold\">Molar Heat Capacities (sum over all species, Cp \u00d7 stoichiometric coefficient)<\/span><\/div><div class=\"field has-term\" id=\"input-7\"><label for=\"field-10\">Sum of Reactant Heat Capacities (\u03a3Cp,reactants)<\/label><div class=\"term\">\u03a3Cp,r<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"sum_of_reactant_heat_capacities_cpreactants\" id=\"field-10\" aria-describedby=\"calc-info-10\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 115.5\" min=\"0\" value=\"115.5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-11\" name=\"unit\" aria-label=\"Unit\"><option value=\"J_molK\" selected>J\/(mol\u00b7K)<\/option><option value=\"kJ_molK\">kJ\/(mol\u00b7K)<\/option><option value=\"cal_molK\">cal\/(mol\u00b7K)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-10\">\u03a3 Cp \u00d7 \u03bd over all reactants. Example N\u2082 + 3H\u2082: 29.1 + 3 \u00d7 28.8 = 115.5 J\/(mol\u00b7K).<\/small><\/div><div class=\"field has-term\" id=\"input-8\"><label for=\"field-12\">Sum of Product Heat Capacities (\u03a3Cp,products)<\/label><div class=\"term\">\u03a3Cp,p<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"sum_of_product_heat_capacities_cpproducts\" id=\"field-12\" aria-describedby=\"calc-info-12\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 71.2\" min=\"0\" value=\"71.2\"\/><div class=\"grid grid-cols-1\"><select id=\"field-13\" name=\"unit\" aria-label=\"Unit\"><option value=\"J_molK\" selected>J\/(mol\u00b7K)<\/option><option value=\"kJ_molK\">kJ\/(mol\u00b7K)<\/option><option value=\"cal_molK\">cal\/(mol\u00b7K)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-12\">\u03a3 Cp \u00d7 \u03bd over all products. Example 2NH\u2083: 2 \u00d7 35.6 = 71.2 J\/(mol\u00b7K).<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66913\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Kirchhoff&#039;s Law Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Reaction Enthalpy at Target Temperature (\u0394H\u2082)<\/span><span class=\"result-term\">\u0394H\u2082<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"kJ\/mol\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>\u0394Cp and Alternative Units<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Calculation Details<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>About Kirchhoff&#039;s Law of Thermochemistry<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"66913\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Kirchhoff's Law of Thermochemistry Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ \\Delta H_2 = \\Delta H_1 + \\Delta C_p \\,(T_2 - T_1) \\\\ \\Delta C_p = \\sum_{\\text{products}} \\nu_i C_{p,i} - \\sum_{\\text{reactants}} \\nu_i C_{p,i} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(\\Delta H_1\\) \u2014 reaction enthalpy at the reference temperature \\(T_1\\) (kJ\/mol)<\/li>\n<li>\\(\\Delta H_2\\) \u2014 reaction enthalpy at the target temperature \\(T_2\\) (kJ\/mol)<\/li>\n<li>\\(\\nu_i\\) \u2014 stoichiometric coefficient of species \\(i\\)<\/li>\n<li>\\(C_{p,i}\\) \u2014 molar heat capacity at constant pressure of species \\(i\\)<\/li>\n<li>\\(\\Delta C_p\\) \u2014 difference between the total heat capacities of products and reactants<\/li>\n<\/ul>\n<p>The formula expresses how a reaction enthalpy changes with temperature: heating (or cooling) the reactants and products by the same amount costs different amounts of heat because their heat capacities differ, and this difference accumulates as the shift in \\(\\Delta H\\). It assumes \\(\\Delta C_p\\) is constant over the interval \\(T_1\\)\u2013\\(T_2\\).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Kirchhoff's Law \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> for the ammonia synthesis reaction N\u2082 + 3H\u2082 \u2192 2NH\u2083, the standard reaction enthalpy at 298.15 K is \u221292.2 kJ\/mol. Estimate the enthalpy at 400 K, using \u03a3Cp(reactants) = 115.5 J\/(mol\u00b7K) (29.1 + 3 \u00d7 28.8) and \u03a3Cp(products) = 71.2 J\/(mol\u00b7K) (2 \u00d7 35.6).<\/p>\n<p>\\[ \\Delta C_p = 71.2 - 115.5 = -44.3\\ \\text{J\/(mol\u00b7K)} = -0.0443\\ \\text{kJ\/(mol\u00b7K)} \\]<\/p>\n<p>\\[ \\Delta H_2 = -92.2 + (-0.0443)(400 - 298.15) = -92.2 - 4.51 = -96.71\\ \\text{kJ\/mol} \\]<\/p>\n<p><strong>Result:<\/strong> \u0394H\u2082 \u2248 \u221296.71 kJ\/mol. The reaction is about 4.5 kJ\/mol more exothermic at 400 K than at 298.15 K because \u0394Cp is negative.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the known <strong>Reaction Enthalpy at Reference Temperature (\u0394H\u2081)<\/strong>, choosing kJ\/mol or kcal\/mol. Use a negative value for an exothermic reaction, a positive value for an endothermic one.<\/li>\n<li>Enter the <strong>Reference Temperature (T\u2081)<\/strong> \u2014 typically 298.15 K \u2014 and select its unit (K, \u00b0C, or \u00b0F).<\/li>\n<li>Enter the <strong>Target Temperature (T\u2082)<\/strong> with its unit. This is the temperature at which you want the adjusted enthalpy.<\/li>\n<li>For every species in the reaction, multiply its molar heat capacity \\(C_p\\) by its stoichiometric coefficient, then sum the values on each side of the equation. Enter the totals as <strong>Sum of Reactant Heat Capacities (\u03a3Cp,reactants)<\/strong> and <strong>Sum of Product Heat Capacities (\u03a3Cp,products)<\/strong>, selecting J\/(mol\u00b7K), kJ\/(mol\u00b7K), or cal\/(mol\u00b7K).<\/li>\n<li>Read the result: the <strong>Reaction Enthalpy at Target Temperature (\u0394H\u2082)<\/strong> in your chosen enthalpy unit, along with \u0394Cp, unit conversions, and a full step-by-step breakdown.<\/li>\n<\/ol>\n<h2>What Is Kirchhoff's Law of Thermochemistry?<\/h2>\n<p>Kirchhoff's law describes how the enthalpy change of a chemical reaction depends on temperature. Because enthalpy is a state function, the temperature derivative of the reaction enthalpy at constant pressure equals the difference in heat capacities between products and reactants:<\/p>\n<p>\\[ \\left( \\frac{\\partial \\Delta H}{\\partial T} \\right)_p = \\Delta C_p \\]<\/p>\n<p>Integrating this expression from \\(T_1\\) to \\(T_2\\) gives \\(\\Delta H(T_2) = \\Delta H(T_1) + \\int_{T_1}^{T_2} \\Delta C_p\\, dT\\). When \\(\\Delta C_p\\) is treated as constant over the temperature interval \u2014 a good approximation for modest ranges \u2014 the integral simplifies to \\(\\Delta C_p (T_2 - T_1)\\), which is the form this calculator uses.<\/p>\n<p>The physical picture is straightforward. Tabulated reaction enthalpies almost always refer to 298.15 K, but real reactors, engines, and calorimeters run at other temperatures. To compare, you imagine heating the reactants from \\(T_1\\) to \\(T_2\\), letting the reaction occur, and cooling the products back \u2014 the difference between the two heating requirements is exactly \\(\\Delta C_p (T_2 - T_1)\\).<\/p>\n<p>Interpreting the sign is the most useful part. If \\(\\Delta C_p &lt; 0\\) (products have lower heat capacity than reactants), the reaction becomes more exothermic as temperature rises. If \\(\\Delta C_p &gt; 0\\), it becomes more endothermic. If \\(\\Delta C_p = 0\\), the enthalpy is independent of temperature. In practice \\(\\Delta C_p\\) is often small, so \\(\\Delta H\\) typically shifts by only a few percent even over hundreds of kelvin.<\/p>\n<h2>Assumptions, Limitations, and Practical Tips<\/h2>\n<ul>\n<li><strong>Constant heat capacities.<\/strong> The linear form is accurate only over intervals where \\(C_p\\) values change little. For wide temperature ranges (more than a few hundred kelvin), use temperature-dependent fits such as \\(C_p = a + bT + cT^2\\) or \\(C_p = a + bT + c\/T^2\\) from standard tables and integrate them instead.<\/li>\n<li><strong>No phase changes.<\/strong> The calculation assumes every species keeps the same phase between \\(T_1\\) and \\(T_2\\). A melting, vaporization, or any other transition inside the interval would add a term \\(\\nu \\Delta H_{\\text{transition}}\\) at the transition temperature.<\/li>\n<li><strong>Consistent data.<\/strong> All heat capacities must refer to the same pressure (usually 1 bar) and the same physical state as the species in the balanced equation. Double-check the stoichiometric coefficients \u2014 the sums \u03a3\u03bdCp must match the equation as written.<\/li>\n<li><strong>Signs matter.<\/strong> Keep \u0394H\u2081 negative for exothermic reactions. The calculator reports whether the reaction is exo- or endothermic at the target temperature and how far the enthalpy shifted.<\/li>\n<li><strong>Watch for T\u2081 = T\u2082.<\/strong> If both temperatures are the same after conversion to kelvin, \u0394H\u2082 simply equals \u0394H\u2081 and the calculator will ask for two different values.<\/li>\n<\/ul>\n<p>If you do not yet have a reference enthalpy, you can build one from standard enthalpies of formation with the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/hesss-law-calculator\/\">Hess's Law calculator<\/a> or estimate it from average bond strengths with the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/reaction-enthalpy-from-bond-energies-calculator\/\">reaction enthalpy from bond energies calculator<\/a>. For other temperature-dependent chemistry estimates, the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/antoine-equation-calculator\/\">Antoine equation calculator<\/a> is a useful companion when vapor pressures are involved.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convert a reaction enthalpy from one temperature to another using Kirchhoff's law. Enter the known enthalpy at a reference temperature, the target temperature, and the summed heat capacities of reactants and products.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[54],"tags":[57],"class_list":["post-66913","post","type-post","status-publish","format-standard","hentry","category-chemistry","tag-reactions"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66913","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=66913"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66913\/revisions"}],"predecessor-version":[{"id":66914,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66913\/revisions\/66914"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66913"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66913"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}